Light scattering from wormlike chains with excluded volume effects

This paper reports a calculation of the angular dependence of light scattering from wormlike chains with excluded volume effects. The Daniels distribution function, modified for excluded volume effects, is used to compute averages for scattering elements separated by contour lengths which are long with respect to the persistence length of the chain. An expansion in terms of exactly known moments of the distribution for the wormlike coil without excluded volume is used for short contour lengths. The results are applied to scattering from calf thymus (M = 18.1 × 10⁶) and T7 (M = 25.4 × 10⁶) DNA. It is demonstrated that the same values of excluded volume parameter (ε = 0.11) and statistical segment length (1/λ′ = 900 Å) which explain the sedimentation and viscosity behavior of DNA also account satisfactorily for the scattering behavior. Molecular weights and root-mean-square radii estimated by extrapolation from scattering data obtained in the angular region from 10° to 25° will be 5–10% too large for DNA of molecular weight 20 × 10⁶–30 × 10⁶.     

Multistep Brownian dynamics: application to short wormlike chains

Brownian dynamics simulations of short wormlike chains are carried out using the method of Ermak and McCammon [(1978) J. Chem. Phys. 69 , 1352–1360]. Following Hagerman and Zimm [(1981) Biopolymers 20 , 1481–1502], the wormlike chain is modeled as a string of beads. In each simulation, the dynamic evolution of an ensemble of 100 randomly generated chains is calculated for a period of from 3 to 200 ns. Two different “experiments,” fluorescence depolarization and dynamic light scattering, were performed in these simulations. Since we are primarily interested in the bending motions and not the torsional motions in this work, we have placed the transition moments along the local symmetry axis of the wormlike chain in the fluorescence depolarization “experiment.” As predicted by the Barkley and Zimm theory [(1979) J. Chem. Phys. 70 , 2991–3008], a considerable amount of rapid bending motion was detected by fluorescence depolarization, though not as much as predicted by theory. We conclude that these differences are primarily due to differences between the model used in the theory and the simulations. The light-scattering experiment was found to be insensitive to internal motion in the low scattering angle limit.     

Asymmetrical-flow field-flow fractionation with on-line multiangle light scattering detection. 1. Application to wormlike chain analysis of weakly stiff polymer chains

Four samples of hyaluronan in the sodium form, ranging in weight-average molecular weight, M(w), from 6.67 x 10(5) to 4.23 x 10(6) were investigated by asymmetrical-flow field-flow fractionation coupled to multiangle light scattering (FlFFF-MALS) in 0.2 M aqueous NaCl at 25 degrees C. M(w) and z-average radii of gyration, R(G)(z)(), obtained via FlFFF-MALS showed a good agreement with the results obtained by conventional static light scattering. Furthermore, the molecular weight dependence of the radius of gyration for sodium hyaluronan obtained via FlFFF-MALS was analyzed on the basis of the Kratky-Porod model for unperturbed wormlike chains combined with the Yamakawa theory for radius expansion factor, and a sufficiently good agreement was observed between the theoretical prediction and experimental data. These results show the potential usage of FlFFF-MALS regarding size separation and molecular characterization even for weakly stiff chains.     

Total lipids with short and long acyl chains from Acholeplasma form nonlamellar phases.

The cell-wall-less bacterium Acholeplasma laidlawii A-EF22 synthesizes eight glycerolipids. Some of them form lamellar phases, whereas others are able to form normal or reversed nonlamellar phases. In this study we examined the phase properties of total lipid extracts with limiting average acyl chain lengths of 15 and 19 carbon atoms. The temperature at which these extracts formed reversed hexagonal (HII) phases differed by 5-10 degreesC when the water contents were 20-30 wt%. Thus the cells adjust the ratio between lamellar-forming and nonlamellar-forming lipids to the acyl chain lengths. Because short acyl chains generally increase the potential of lipids to form bilayers, it was judged interesting to determine which of the A. laidlawii A lipids are able to form reversed nonlamellar phases with short acyl chains. The two candidates with this ability are monoacyldiglucosyldiacylglycerol (MADGlcDAG) and monoglucosyldiacylglycerol. The average acyl chain lengths were 14.7 and 15.1 carbon atoms, and the degrees of acyl chain unsaturation were 32 and 46 mol%, respectively. The only liquid crystalline phase formed by MADGlcDAG is an HII phase. Monoglucosyldiacylglycerol forms reversed cubic (Ia3d) and HII phases at high temperatures. Thus, even when the organism is grown with short fatty acids, it synthesizes two lipids that have the capacity to maintain the nonlamellar tendency of the lipid bilayer. MADGlcDAG in particular contributes very powerfully to this tendency.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

The correlation of human erythrocyte shape with dark-field light scattering intensity]

This study was concerned with the quantitative evaluation of dark field light scattering by sedimented erythrocytes of banked human blood samples. Due to considerable variability of both appearance and amount of scattered light the discocyte group had to be subdivided into discocyte I and discocyte II. The mean intensity of scattered light increased about three fold from discocyte II to echinocytes I, II, III, sphaeroechinocyte, and sphaerocyte. On the other hand the average light scattering intensity of discocytes I exceeded that of discocytes II about 2.5 times, with individual data varying over a wide range. There was a rapid disappearing of discocytes I correlated with time of storage. Therefore it is concluded that discocytes I represent the initial stage of erythrocytes transforming under banking conditions.     

On intensity reinforcements in small-angle light scattering patterns of erythrocytes under shear

On small-angle light scattering patterns obtained with erythrocytes under shear, intensity reinforcements in rings can be noticed. Why should one be interested in them and how does one explain their presence? After examining several hypotheses, analysis shows that this is the consequence of a shape effect: The red cells under stress are not three-axis ellipsoids but rather ellipsoid-like particles whose extremities are thinned.     

Quasielastic light scattering from migrating chemotactic bands of Escherichia coli. II. Analysis of anisotropic bacterial motions.

Chemotactic effects of dissolved oxygen on motions of Escherichia coli in a motility buffer solution have been studied by measurements of quasielastic light scattering. Under conditions where the bacteria form a sharp band in an oxygen concentrations gradient created by their metabolism, components of motions along the direction of the gradient and perpendicular to it were studied separately at each point within the band profile. A theoretical model for bacterial self correlation function based on two-state motions has been developed to extract the mean square speed of run motion and the relative probability of twiddle vs. run at each point of the band profile. A combined novel experimental set-up and new data analysis method allowed us to extract also the mean square displacements at short times along and perpendicular to the direction of the gradient. Parameters extracted from the measured correlation functions have been discussed in the framework of the established picture of bacterial motions under chemotaxis.     

Theory of light scattering from hollow spheres

Light-scattering from a dilute, fluid disperson of rigid, hollow spheres is treated in the Rayleigh—Debye approximation. The hollow spheres are composed of cylindrically symmetric, radially oriented scattering elements. Analytic expressions for all form factors are derived. The time correlation function of the scattered intensity depends only on the translational diffusion coefficient of the sphere.     

Statistical length of DNA from light scattering

An analysis of hydrodynamic data of DNA by use of the wormlike coil model gave a statistical length of 1300 Å, in the absence of excluded volume corrections. The worm-like coil model and this hydrodynamically observed statistical length adequately describe the light scattering properties of DNA.     

Quasielastic light scattering from long rigid rods

The purpose of this work was to improve our understanding of quasielastic light scattering from long rigid rods (QL >> 1). For these scatterers, only small angular displacements are required to produce dephasing of the scattering light. This plus the fact that only rods lying perpendicular to Q contribute to the scattered light allow one to simplify the intermediate scattering function to an analytic form. This form is shown to be nonexponential, exhibiting (t)^?½ behavior at long delay times. This new scattering function can then be fit to experimental functions using standard methods.     

Static and dynamic light scattering from aggregating particles

We use standard hydrodynamic and light scattering theories to calculate the total intensity and dynamic light scattering properties of random aggregates of spherical particles containing up to ten spheres. When the aggregates have dimensions comparable to the wavelength of light, intraaggregate interference effects can dramatically reduce the apparent size of the aggregates. These results could be significant in interpreting DNA condensation, protein polymerization, and other biomolecular aggregation reactions.     

Dynamic light scattering from solutions of microtubules.

Calf brain microtubule protein was assembled in vitro to form dilute solutions of microtubules (240 A diameter) having lengths greater than 1 micrometer. The microtubule solutions were examined by dynamic laser light scattering techniques. The angular dependence of the correlation function leads to the conclusion that the correlation function is measuring the translational diffusion constant of the particles. The length dependence of the correlation function, however, shows that the translational diffusion constant is not being measured and that the diffusion constant for the microtubules cannot be straightforwardly determined. These results suggest that a collective property of the rods is being measured by the laser light scattering. Although specific microtubule-microtubule interactions are a possible explanation for the observed results, we present arguments that suggest that the solution can be adequately modeled as a network of entangled polymers.